A machine tool and a method for aligning a workpiece with an axis of rotation of the machine tool that accommodates the workpiece defined by a hollow shaft including an annular workpiece contour extending a length of the workpiece. The workpiece is clamped to a chuck and supported by clamping supports that engage the outer surface of the workpiece. A moveable tool carrier supports at least one sensor and is operable to position the sensor in proximity to the annular workpiece contour along its length. The sensor measures a distance between the sensor and the workpiece contour over a plurality of defined angles of the annular workpiece contour and at a plurality of locations along the length to obtain measurement data that is used to determine an approximated longitudinal central axis of the workpiece that is aligned with the axis of rotation of the machine tool.